List of publications cited in the 2019 FDEPS Course
Convection in solid planetary interiors and implications
for their evolution
Stéphane Labrosse, ENS Lyon, France
November 26-29, 2019

Part I. Fundamentals of Rayleigh-Bénard convectionBénard, H. (1900a). Les tourbillons celullaires dans une nappe liquide. Deuxième partie : procédésmécaniques et optiques d’examen. Lois numériques des phénomènes. 12: 1309–1328.
Bénard, H. (1900b). Les tourbillons celullaires dans une nappe liquide. Première partie : descriptiongénérale des phénomènes. 12: 1261–1271.
Bénard, H. (1901). Les tourbillons celullaires dans une nappe liquide transportant la chaleur par convection
en régime permanent. Ann. Chim. Phys. 23: 62–144.
Block, M. J. (1956). Surface Tension as the Cause of Bénard Cells and Surface Deformation in a Liquid
Film. Nature 178: 650–651.
Boussinesq, J. (1903). Théorie Analytique de la Chaleur. Vol. 2. pp. 157–161. Gauthier-Villars.
Busse, F. H. (1967). On the stability of two-dimensional convection in a layer heated from below. J. Math.
and Phys. 46: 140–149.
Busse, F. H. and J. A. Whitehead (1971). Instabilities of convection rolls in a high Prandtl number fluid.
J. Fluid Mech. 47: 305–320.
Grigné, C., S. Labrosse, and P. J. Tackley (2007a). Convection under a lid of finite conductivity in wide
aspect ratio models: eﬀect of continents on the wavelength of mantle flow. J. Geophys. Res. 112:
B08403.References II
Grigné, C., S. Labrosse, and P. J. Tackley (2007b). Convection under a lid of finite conductivity: Heat flux
scaling and application to continents. J. Geophys. Res. 112: B08402.
Guo, W., G. Labrosse, and R. Narayanan (2012). The Application of the Chebyshev-Spectral Method inTransport Phenomena. Berlin: Springer-Verlag.
Howard, L. N. (1964).

Convection at High Rayleigh number . Proceedings of the Eleventh International

Congress of Applied Mechanics. Ed. by H. Gortler. New York: Springer-Verlag, 1109–1115.
Krishnamurti, R. (1973). Some further studies on the transition to turbulent convection. J. Fluid Mech.
60: 285–303.
Labrosse, S., A. Morison, R. Deguen, and T. Alboussière (2018). Rayleigh-Bénard convection in a creeping
solid with a phase change at either or both horizontal boundaries. J. Fluid Mech. 846: 5–36.
Malkus, W. and G. Veronis (1958). Finite amplitude cellular convection. J. Fluid Mech. 4: 225–260.
Manneville, P. (2004). Instabilities, Chaos and Turbulence - An introduction to nonlinear dynamics andcomplex systems. London: Imperial College Press.
Niemela, J. J., L. Skrbek, K. R. Sreenivasan, and R. J. Donnelly (2000). Turbulent convection at very highRayleigh numbers. Nature 404: 837–841.References III
Oberbeck, A. (1879). ber die Wrmeleitung des Flssigkeiten bei Bercksichtigung des Strmungen infolge vonTemperaturdiﬀerenzen. Ann. Phys. Chem. 7: 271–292.
Pearson (1958). On convection cells induced by surface tension. J. Fluid Mech. 4: 489–500.
Pouilloux, L., E. Kaminski, and S. Labrosse (2007). Anisotropic rheology of a cubic medium and implications for geological materials. Geophysical Journal International 170: 876–885.

Rayleigh, L. (1916). On convection currents in a horizontal layer of fluid, when the higher temperature ison the under side. Phil. Mag. 32: 529–546.
Ricard, Y., S. Labrosse, and F. Dubuﬀet (2014). Lifting the cover of the cauldron: Convection in hot
planets. Geochem. Geophys. Geosyst. 15: 4617–4630.
Schlter, A., D. Lortz, and F. Busse (1965). On the Stability of Steady Finite Amplitude Convection. J.
Fluid Mech. 23: 129–144.
Sotin, C. and S. Labrosse (1999). Three-dimensional Thermal convection of an isoviscous, infinite–Prandtl–
number fluid heated from within and from below: applications to heat transfer in planetary mantles.
Phys. Earth Planet. Inter. 112: 171–190.

Part II. Convection in Earth’s mantle
Albarède, F., and R. D. van der Hilst (2002). Zoned mantle convection. Philosophical Transactions of
the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 360(1800):
2569–2592.
Andrault, D., G. Pesce, M. A. Bouhifd, N. Bolfan-Casanova, J.-M. Hénot, and M. Mezouar (2014). Meltingof subducted basalt at the core-mantle boundary. Science 344: 892–895.
Ballmer, M. D., L. Schumacher, V. Lekic, C. Thomas, and G. Ito (2016). Compositional layering within thelarge low shear ‐ wave velocity provinces in the lower mantle. Geochemistry, Geophysics, Geosystems,
17(12): 5056–5077.
Ballmer, M. D., C. Houser, J. W. Hernlund, R. M. Wentzcovitch, and K. Hirose (2017). Persistence ofstrong silica-enriched domains in the Earth’s lower mantle. Nature Geoscience, 10(3): 236.
Becker, T. W. and L. Boschi (2002). A comparison of tomographic and geodynamic mantle models.
Geochem. Geophys. Geosyst. 3:
Bercovici, D. and S.-i. Karato (2003). Whole-mantle convection and the transitionzone water filter. Nature
425: 39–44.
Bercovici, D. and Y. R. Ricard (2014). Plate tectonics, damage and inheritance. Nature 508: 513–516.
Burke, K., and T. H. Torsvik (2004). Derivation of large igneous provinces of the past 200 million years
from long-term heterogeneities in the deep mantle. Earth and Planetary Science Letters, 227(3–4):
531–538.
Carlson, R. L. and H. P. Johnson (1994). on modeling the thermal evolution of the oceanic upper-mantle: anassessment of the cooling plate model on modeling the thermal evolution of the oceanic upper-mantle:
an assessment of the cooling plate model. J. Geophys. Res. 99: 3201–3214.
Christensen, U. R. and A. W. Hofmann (1994). Segregation of subducted oceanic crust in the convecting
mantle. J. Geophys. Res. 99: 19867–19884.
Cogné, J.-P. and E. Humler (2004). Temporal variation of oceanic spreading and crustal production rates
during the last 180 My. Earth Planet. Sci. Lett. 227: (3-4), 427–439.
Coltice, N., T. Rolf, P. J. Tackley, and S. Labrosse (2012). Dynamic Causes of the Relation Between Area
and Age of the Ocean Floor. Science 336: 335–338.References II
Curbelo, J., L. Duarte, T. Alboussière, F. Dubuﬀet, S. Labrosse, and Y. Ricard (2019). Numerical solutionsof compressible convection with an infinite Prandtl number: comparison of the anelastic and anelastic
liquid models with the exact equations Compressible convection with infinite Prandtl number. J. Fluid
Mech 873: 646–687.
Davaille, A. and C. Jaupart (1993). Transient high-Rayleigh-number thermal convection with large viscosity
variations. J. Fluid Mech. 253: 141–166.
Davaille, A. and C. Jaupart (1994). Onset of thermal convection in fluids with temperature-dependent

viscosity: Application to the oceanic mantle. J. Geophys. Res. 99: 19853–19866.
Davaille, A. (1999). Simultaneous Generation of Hotspots and Superswells by Convection in a Heterogeneous Planetary Mantle. Nature 402: 756–760.
Davis, E. E., D. S. Chapman, K. Wand, H. Villinger, A. T. Fisher, S. W. Robinson, J. Grigel, D. Pribnow,
J. Stein, and K. Becker (1999). Regional heat flow variations across the sedimented Juan de Fuca ridge
eastern flank: constraints on lithospheric cooling and lateral hydrothermal heat transport. J. Geophys.
Res. 104: 17, 675–17, 688.
Dumoulin, C., D. Bercovici, and P. Wessel (1998). A continuous plate tectonic model using geophysicaldata to estimate plate-margin widths, with a seismicity-based example. Geophys. J. Int. 133: 379–
389.References III
Grigné, C., S. Labrosse, and P. J. Tackley (2005). Convective heat transfer as a function of wavelength:
Implications for the cooling of the Earth. J. Geophys. Res. 110: doi:10.1029/2004JB003376, B03409.
Grigné, C., S. Labrosse, and P. J. Tackley (2007a). Convection under a lid of finite conductivity in wide
aspect ratio models: eﬀect of continents on the wavelength of mantle flow. J. Geophys. Res. 112:
B08403.
Grigné, C., S. Labrosse, and P. J. Tackley (2007b). Convection under a lid of finite conductivity: Heat flux
scaling and application to continents. J. Geophys. Res. 112: B08402.
Guillou, L. and C. Jaupart (1995). On the eﬀect of continents on mantle convection. J. Geophys. Res.
100: 24217–24238.
Gurnis, M. (1988). Large-Scale Mantle Convection and the Aggregation and Dispersal of Supercontinents.
Nature 332: 695–699.
Hernlund, J. W., and A. K. McNamara (2015). The coremantle boundary region. In Schubert, G. (eds.)
Treatise on Geophysics (2nd ed.). Elsevier: 461–519.
Jaupart, C., S. Labrosse, F. Lucazeau, and J.-C. Mareschal (2015).

7.06 - Temperatures, Heat, andEnergy in the Mantle of the Earth . Treatise on Geophysics (Second Edition). Ed. by G. Schubert.
Second Edition. Oxford: Elsevier, 223–270.
Jeﬀreys, H. (1930). The instability of a compressible fluid heated below. Math. Proc. Camb. Phil. Soc.
26: 170–172.
Kanda, R. V. and D. J. Stevenson (2006). Suction mechanism for iron entrainment into the lower mantle.
Geophys. Res. Lett. 33: 4–7.References IV
Koelemeijer, P., A. Deuss, and J. Ritsema (2017). Density structure of Earth’s lowermost mantle from
Stoneley mode splitting observations. Nature Communications 8: 1–10.
Kingston Tivey, M. (2004). Environmental conditions within active seafloor vent structures: sensitivity
to vent fluid composition and fluid flow. Washington DC American Geophysical Union Geophysical
Monograph Series, 144: 137–152.
Krishnamurti, R. (1968). Finite Amplitude Convection With Changing Mean Temperature. Part 1. Theory. J. Fluid Mech. 33: 445–455.
Labrosse, S. and C. Jaupart (2007). Thermal Evolution of the Earth: Secular Changes and Fluctuationsof Plate Characteristics. Earth Planet. Sci. Lett. 260: 465–481.
Le Bars, M. and A. Davaille (2004). Whole layer convection in a heterogeneous planetary mantle. J.
Geophys. Res. 109: doi:10.1029/2003JB002617, B03403.
Leng, W. and S. Zhong (2008). Viscous heating, adiabatic heating and energetic consistency in compressible
mantle convection. Geophysical Journal International 173: 693–702.
Li, M. and A. K. McNamara (2013). The diﬃculty for subducted oceanic crust to accumulate at the Earth’s
core-mantle boundary. J. Geophys. Res. 118: 1807–1816.

Li, M., A. K. McNamara, and E. J. Garnero (2014). Chemical complexity of hotspots caused by cycling
oceanic crust through mantle reservoirs. Nature Geoscience 7: 366–370.References V
Lister, C. R. B., J. G. Sclater, E. E. Davis, H. Villinger, and S. Nagihara (1990). Heat flow maintained inocean basins of great age: investigations in the north-equatorial West Pacific. GJI 102: 603–628.
McNamara, A. K., E. J. Garnero, and S. Rost (2010). Tracking deep mantle reservoirs with ultra-low
velocity zones. Earth and Planetary Science Letters, 299(1-2): 1–9.
Moreira, M. (2013). Noble gas constraints on the origin and evolution of Earth s volatiles. Geochemical
Perspectives, 2(2): 229–230.
Moresi, L. N. and V. S. Solomatov (1995). Numerical investigation of 2D convection with extremely large
viscosity variations. Phys. Fluids 7: 2154–2162.
Müller, R. D., M. Sdrolias, C. Gaina, and W. R. Roest (2008). Age, spreading rates, and spreading
asymmetry of the world’s ocean crust. Geochemistry, Geophysics, Geosystems: 9(4).
Nakagawa, T. and P. J. Tackley (2018). Lateral variations in CMB heat flux and deep mantle seismic
velocity caused by a thermal-chemical-phase boundary layer in 3D spherical convection. Earth Planet.
Sci. Lett. 271: 348–358.
Otsuka, K. and S. I. Karato (2012). Deep penetration of molten iron into the mantle caused by a morphological instability. Nature 492: 243–246.
Parmentier, E. M. and C. Sotin (2000). Three-dimensional numerical experiments on thermal convection
in a very viscous fluid: Implications for the dynamics of a thermal boundary layer at high Rayleighnumber. Phys. Fluids 12: 609–617.
Pouilloux, L., E. Kaminski, and S. Labrosse (2007). Anisotropic rheology of a cubic medium and implications for geological materials. Geophysical Journal International 170: 876–885.
Rayleigh, L. (1916). On convection currents in a horizontal layer of fluid, when the higher temperature ison the under side. Phil. Mag. 32: 529–546.
Ribe, N. M. (2018). Theoretical mantle dynamics. Cambridge University Press.References VI
Ricard, Y., M. Richards, C. Lithgow-Bertelloni, and Y. LeStunﬀ (1993). A Geodynamic Model Of Mantle
Density Heterogeneity. J. Geophys. Res. 98: 21895–21909.
Ritsema, J., H. J. v. Heijst, and J. H. Woodhouse (1999). Complex Shear Wave Velocity Structure Imaged
Beneath Africa and Iceland. Science 286: 1925–1928. eprint:
http://www.sciencemag.org/cgi/reprint/286/5446/1925.pdf.
Sanloup, C., J. W. E. Drewitt, Z. Konôpková, P. Dalladay-Simpson, D. M. Morton, N. Rai, W. van
Westrenen, and W. Morgenroth (2013). Structural change in molten basalt at deep mantle conditions.
Nature 503: 104–107.
Smith, W. H. F. and D. T. Sandwell (1997). Global Sea Floor Topography from Satellite Altimetry andShip Depth Soundings. Science 277: 1956–1962. eprint:
http://science.sciencemag.org/content/277/5334/1956.full.pdf.
Sotin, C. and S. Labrosse (1999). Three-dimensional Thermal convection of an isoviscous, infinite-Prandtlnumber fluid heated from within and from below: applications to heat transfer in planetary mantles.
Phys. Earth Planet. Inter. 112: 171–190.References VII
Tackley, P. J. (2000).

Self-Consistent Generation of Tectonic Plates in Time-Dependent, Three-

Dimensional Mantle Convection Simulations 1. Pseudoplastic yielding. Geochem. Geophys. Geosyst.
1: 2000Gc000041.
Vine, F. J. (1966). Spreading of the ocean floor: new evidence. Science, 154(3755): 1405–1415.
White, D. B. (1988). The Planforms And Onset Of Convection With A Temperature-Dependent Viscosity.
J. Fluid Mech. 191: 247–286.

Part III. Application to the thermal evolution of the EarthAbe, Y. (1997). Thermal and chemical evolution of the terrestrial magma ocean. Phys. Earth Planet.
Inter. 100: 27–39.
Christensen, U. R. (1985). Thermal evolution models for the Earth, J. Geophys. Res. 90: 2995–3007.
Conrad, C. P., and B. H. Hager (1999). The thermal evolution of an Earth with strong subduction zones.
Geophys. Res. Lett. 26: 3041–3044.
Conrad, C. P., and B. H. Hager (2001). Mantle convection with strong subduction zones, Geophys. J. Int.,
144, 271–288.
Hernlund, J. W., C. Thomas, and P. J. Tackley (2005). A doubling of the post-perovskite phase boundaryand structure of the Earth’s lowermost mantle. Nature 434: 882–886.
Korenaga, J. (2003). Energetics of mantle convection and the fate of fossil heat. Geophys. Res. Lett. 30.
Labrosse, S., J. W. Hernlund, and N. Coltice (2007). A Crystallizing Dense Magma Ocean at the Base of
Earth’s Mantle. Nature 450: 866–869.
McKenzie, D. P. and F. M. Richter (1981). parameterized thermal convection in a layered region and thethermal history of the Earth. J. Geophys. Res. 86: 11667–11680.
McNamara, A. K., E. J. Garnero, and S. Rost (2010). Tracking deep mantle reservoirs with ultra-low
velocity zones. Earth and Planetary Science Letters, 299(1-2): 1–9.
Schubert, G. and T. Spohn (1981). Two-Layer Mantle Convection and the Depletion of Radioactive
Elements in the Lower Mantle. Geophys. Res. Lett. 8: 951–954.
Sleep, N. H. (2000). Evolution of the Mode of Convection within Terrestrial Planets. J. Geophys. Res.
105: 17563–17578.

Part IV. Convection in solid shells with solid–liquid phase change
at the boundaryAbe, Y. (1997). Thermal and chemical evolution of the terrestrial magma ocean, Physics of the Earth andPlanetary Interiors, 100, 27–39.
Agrusta, R., A. Morison, S. Labrosse, R. Deguen, T. Alboussière, P. J. Tackley, and F. Dubuﬀet (2019).
Mantle convection interacting with magma oceans. Geophys. J. Int. in press.
Alboussière, T., R. Deguen, and M. Melzani (2010). Melting-induced stratification above the Earth s
inner core due to convective translation. Nature 466: 744–747.
Aubert, J., H. Amit, G. Hulot, and P. Olson (2008). Thermochemical flows couple the Earth s inner core
growth to mantle heterogeneity. Nature 454: 758.
Bergman, M. I. (1997). Measurements of elastic anisotropy due to solidification texturing and the implications for the Earth s inner core. Nature 389: 60–63.
Bergman, M. I., D. M. Cole, and J. R. Jones (2002). Preferred crystal orientations due to melt convection
during directional solidification. J. Geophys. Res. 107: ECV 6–1–ECV 6–8.
Buﬀett, B. A. and J. Bloxham (2000). Deformation of Earth s inner core by electromagnetic forces.
Geophys. Res. Lett. 27: 4001–4004.
Buﬀett, B. A. and H.-R. Wenk (2001). Texturing of the Earth s inner core by Maxwell stresses. Nature
413: 60–63.
Deguen, R., T. Alboussière, and P. Cardin (2013). Thermal convection in Earth s inner core with phasechange at its boundary. Geophys. J. Int. 194: 1310–1334.
Deguen, R., T. Alboussière, and S. Labrosse (2018). Double-diﬀusive translation of Earth s inner core.
Geophys. J. Int. 214: 88–107.References II

Deguen, R. and P. Cardin (2011). Thermochemical convection in Earth s inner core. Geophys. J. Int.
187: 1101–1118.
Gomi, H., K. Ohta, K. Hirose, S. Labrosse, R. Caracas, M. J. Verstraete, and J. W. Hernlund (2013). The
high conductivity of iron and thermal evolution of the Earth s Core. Phys. Earth Planet. Inter. 224:
88–103.
Gubbins, D., D. Alfè, and C. J. Davies (2013). Compositional instability of Earth s solid inner core.
Geophys. Res. Lett. 40: 1084–1088.
Hernlund, J. W. and P. J. Tackley (2008). Modeling mantle convection in the spherical annulus. Phys.
Earth Planet. Inter. 171: 48–54.
Ishiwatari, M., S.-I. Takehiro, and Y.-Y. Hayashi (1994). The eﬀects of thermal conditions on the cell sizesof two-dimensional convection. J. Fluid Mech. 281: 33–50.
Jacobs, J. A. (1953). The Earth s inner core. Nature 172: 297–298.
Jeanloz, R. and H.-R. Wenk (1988). Convection and anisotropy of the inner core. Geophys. Res. Lett. 15:
72–75.
Karato, S. (1999). Seismic anisotropy of the Earth’s inner core resulting from flow induced by Maxwell
stresses. Nature 402, 871–873.
Karato, S. (1993). Inner core anisotropy due to the magnetic flied-induces preferred orientation of iron.
Science 262: 1708–1711.References III
Koker, N. de, G. Steinle-Neumann, and V. Vlček (2012). Electrical resistivity and thermal conductivity ofliquid Fe alloys at high P and T, and heat flux in Earth s core. Proc. Nat. Acad. Sci. U.S.A. 109:
4070–4073.
Labrosse, S. (2014). Thermal and compositional stratification of the inner core. C. R. Geosciences 346:
119–129.
Labrosse, S., J.-P. Poirier, and J.-L. Le Mouël (1997). On cooling of the Earth s Core. Phys. Earth
Planet. Inter. 99: 1–17.
Labrosse, S., A. Morison, R. Deguen, and T. Alboussière (2018). Rayleigh-Bénard convection in a creeping
solid with a phase change at either or both horizontal boundaries. J. Fluid Mech. 846: 5–36.
Lasbleis, M. and R. Deguen (2015). Building a regime diagram for the Earth s inner core. Phys. Earth
Planet. Inter. 247: 80–93.
Mizzon, H. and M. Monnereau (2013). Implication of the lopsided growth for the viscosity of Earth s
inner core. Earth Planet. Sci. Lett. 361: 391–401.
Morelli, A., A. M. Dziewonski, and J. H. Woodhouse (1986). Anisotropy of the inner core inferred fromPKIKP travel times. Geophys. Res. Lett. 13: 1545–1548.
Morison, A., S. Labrosse, R. Deguen, and T. Alboussière (2019). Timescale of overturn in a magma ocean
cumulate. Earth Planet. Sci. Lett. 516: 25–36.References IV
Poupinet, G., R. Pillet, and A. Souriau (1983). Possible heterogeneity of the Earth s core deduced fromPKIKP travel times. Nature 305: 204–206.
Pozzo, M., C. J. Davies, D. Gubbins, and D. Alfè (2012). Thermal and electrical conductivity of iron at
Earth s core conditions. Nature 485: 355–358.
Tackley, P. J. (2008). Modelling compressible mantle convection with large viscosity contrasts in a threedimensional spherical shell using the yin-yang grid. Phys. Earth Planet. Inter. 171: 7–18.
Takehiro, S.-I. (2011). Fluid motions induced by horizontally heterogeneous Joule heating in the Earth s
inner core. Phys. Earth Planet. Inter. 184: 134–142.
Takehiro, S.-i., M. Ishiwatari, K. Nakajima, and Y.-Y. Hayashi (2002). Linear Stability of Thermal Convection in Rotating Systems with Fixed Heat Flux Boundaries. Geophys. Astrophys. Fluid Dyn 96:

439–459.
Tectonic history of the Earth s inner core preserved in its seismic structure (2009). Nature Geosci 2:
419–422.
Weber, P. and P. Machetel (1992). Convection within the inner-core and thermal implications. Geophys.
Res. Lett. 19: 2107–2110.
Woodhouse, J. H., D. Giardini, and X.-D. Li (1986). Evidence for inner core anisotropy from free oscillations. Geophys. Res. Lett. 13: 1549–1552.References V
Yoshida, S., I. Sumita, and M. Kumazawa (1996). Growth model of the inner core coupled with the outer
core dynamics and the resulting elastic anisotropy. J. Geophys. Res. 101: 28085–28103.

Research Seminar
Abe, Y. (1997). Thermal and chemical evolution of the terrestrial magma ocean, Physics of the Earth andPlanetary Interiors, 100, 27–39.
Andrault, D., G. Pesce, M. A. Bouhifd, N. Bolfan-Casanova, J.-M. Hénot, and M. Mezouar (2014). Meltingof subducted basalt at the core-mantle boundary. Science 344: 892–895.
Andrault, D., S. Petitgirard, G. Lo Nigro, J.-L. Devidal, G. Veronesi, and G. Garbarino (2012). Solid-liquid
iron partitioning in Earth’s deep mantle, Nature, 487: 354–357.
Conrad, C. P. and B. H. Hager (1999). Thermal evolution of an Earth with strong subduction zones.
Geophys. Res. Lett. 26: 3041–3044.
French, S. W. and B. Romanowicz (2015). Broad plumes rooted at the base of the Earth’s mantle beneath
major hotspots. Nature 525: 95–99.
Grigné, C., S. Labrosse, and P. J. Tackley (2005). Convective heat transfer as a function of wavelength:
Implications for the cooling of the Earth. J. Geophys. Res. 110: doi:10.1029/2004JB003376, B03409.
Hirose, K., G. Morard, R. Sinmyo, K. Umemoto, J. Hernlund, G. Helﬀrich, and S. Labrosse (2017).
Crystallization of silicon dioxide and compositional evolution of the Earth’s core. Nature. 543: 99.
Korenaga, J. (2003) Energetics of mantle convection and the fate of fossil heat. Geophys. Res. Lett. 30:
1437.
Labrosse, S., J. W. Hernlund, and N. Coltice (2007). A Crystallizing Dense Magma Ocean at the Base of
Earth’s Mantle. Nature 450: 866–869.
McKenzie, D. P. and F. M. Richter (1981). parameterized thermal convection in a layered region and thethermal history of the Earth. J. Geophys. Res. 86: 11667–11680.
McNamara, A. K., E. J. Garnero and S. Rost (2010). Tracking deep mantle reservoirs with ultra-low
velocity zones. Earth Planet. Sci. Lett. 299: 1–9.
Schubert, G. and T. Spohn (1981). Two-Layer Mantle Convection and the Depletion of Radioactive
Elements in the Lower Mantle. Geophys. Res. Lett. 8: 951–954.
Sleep, N. H. (2000). Evolution of the Mode of Convection within Terrestrial Planets. J. Geophys. Res.
105: 17563–17578.
Spohn, T. and G. Schubert (1982). Modes of mantle convection and the removal of heat from the Earth’s
interior, J. geophys. Res., 87: 4682–4696.